%\begin{exercise}
%ex6-5
%\end{exercise}

\begin{proof}
Since the edges of a graph and its automorphism are same, total edges of the complete graph be composed of both of them must be even.However, a graph consists of 999 vertices has $C_{999}^2=498501$ edges, which is odd. So there is no self-complementary graph on 999 vertices.
\end{proof}

%\begin{exercise}
%ex6-6
%\end{exercise}

%Answer: $n=4k\: or\: 4k+1$
%\begin{proof}
%Maybe we can prove it by adjacent matrix.
%\end{proof}
